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Uncertainties enter into a complex problem from many sources: variability, errors, and lack of knowledge. A fundamental question arises in how to characterize the various kinds of uncertainty and then combine within a problem such as the verification and validation of a computer model, reliability of a dynamic system, or a complex decision problem. Our aim is to explore how probability theory and fuzzy set theory can be made to work in concert, so that uncertainty of outcomes and imprecision can be treated in a unified and coherent manner. Both the theoretical and application of a linkage between the two ...
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Description

Uncertainties enter into a complex problem from many sources: variability, errors, and lack of knowledge. A fundamental question arises in how to characterize the various kinds of uncertainty and then combine within a problem such as the verification and validation of a computer model, reliability of a dynamic system, or a complex decision problem. Our aim is to explore how probability theory and fuzzy set theory can be made to work in concert, so that uncertainty of outcomes and imprecision can be treated in a unified and coherent manner. Both the theoretical and application of a linkage between the two theories will be presented. An example from a reliability application will illustrate how the linkage between the theories is accomplished through the use of Bayes Theorem and the probability of fuzzy sets.

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